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20 January, 13:26

When reaching a boundary between two media (1 and 2), an incident ray is partially reflected and partially refracted. The ray is travelling from media 1 to media 2.

At what angle of incidence is the reflected ray perpendicular to the incident ray? The indexes of refraction for the two media are n1 and n2, respectively.

Express your answer in terms of the variables n1 and n2

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  1. 20 January, 15:44
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    Answer: critical angle, sin^-1 (n2/n1)

    Explanation: the angle of incidence at which the retracted ray makes an angle of 90° with the normal is known as the critical angle.

    Snell's law defined refraction mathematically as shown below

    n1 sin θi = n2 sin θr

    n1 = refractive index of the first medium

    n2 = refractive index of the second medium

    θi = angle of incidence

    θr = angle of refraction

    When the refrafted ray is perpendicular to the normal, the angle of refraction (θr) is 90° hence making the angle of incidence (θi) the critical angle θc

    By substituting these conditions into the Snell's law, we have that

    n1 sin θc = n2 sin 90

    According to trigonometry, the value of sin 90 is 1, hence we have that

    n1 sin θc = n2

    sin θc = n2/n1

    θc = sin^-1 (n2/n1)
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